Blair was to hold talks with British and US military chiefs in the British-controlled city of Basra to discuss the way forward.
Tight security surrounded Blair's fourth visit to Iraq since the March 2003 invasion, with a news blackout in place until he touched down from Kuwait on a Hercules transporter, for fear of attacks by armed groups.
"We are getting an assessment on the general election situation - as much as we know - and a military assessment of the security situation," Blair's spokesman told reporters before reaching Iraq's second city.
"First of all, the election results come in, secondly there is a new government agreed. That government then has to take a view on the process of Iraqi-isation. Then we're in a better position to talk about what happens to our troops," he added.
"Iraqi-isation" is London's term for training Iraqi forces to take control of their own security.
British officials will not publicly discuss a timetable for troop withdrawal but they see the election as the latest step on the long road to an eventual pull-out of Britain's 8000 troops.
British troops are based in Basra
London has said it could start scaling down troops next year but officials stress soldiers will only leave when Iraqis are capable of protecting the country from the violent insurgency that has plagued the war's aftermath.
A partial withdrawal of British troops could help ease some pressure on Blair over the US-led conflict.
Blair's support for the invasion has been the most contentious and politically damaging foreign policy decision of his eight-year premiership and has proved a running sore.
Ongoing violence and further British fatalities - 98 UK personnel have been killed since the war began - gives ammunition to opponents who accuse Blair of waging an illegal war, after no weapons of mass destruction were found in Iraq.
London sent some 45,000 soldiers to support the conflict, its biggest deployment since the Korean war half a century ago.
After talks on the election, security and troops with British and US military chiefs, the US ambassador to Iraq Zalmay Khalilzad and London's deputy ambassador Tim Torlot, Blair was due to greet British troops.
He made a similar trip at Christmas last year.